Question

Show the processs

Answer 1

To answer the question, we must know the property of delta (t) function delta(t) is defined as show in below figure delta (t) has area of 1 unit, where height & width are 1/Delta & Delta respectively, as Delta rightarrow 0: so: as Delta rightarrow 0, width decreases, but its strength appears as an impulse delta (t) function helps us to realize ideal capacitor, inductor so let us consider a function x(t) integral^+ infinity_- infinity x(t) delta (t) dt = x (0) (Because integral^infinity_- infinity delta (t) dt = 1: integral^infinity_- infinity x (t) delta (t) dt = x(0) integral^infinity_- infinity delta (t) dt = x (0)) a integral^+ infinity_- infinity cos (2 pi t�) delta (t�) dt� = cos (2 pi (0)) = cos (0) = 1 b integral^0^-_infinity e^- t� delta (t�) dt� = 0 \r\n c integral^+ infinity_0^- rect (t� - 5/4) delta (t� - 5) dt� = we use the property mentioned above: solving above problem